How to align mesh for Seamless Texture Baking?
Two things to make it work.

1. Make your camera Orthographic
This will help you avoid distortion in corners, and will make it 'infinitely flat'.
It's like using an infinitely long lens.



2. Make the array 1:1 aspect ratio
Your chainmail array is ever so slightly taller-than-wide.
Move the rings a bit along the X axis, so they fit nicely.

Voilá. Seamless.

 

Notes
If you want the mail evenly-spaced, you'll have to adjust the whole array (I was just lazy).
I also moved the camera a bit, instead of moving the whole array.  

Adjusted .blendfile is here